High-post-Newtonian-order dynamical effects induced by tail-of-tail interactions in a two-body system

Starting from the recently derived conservative tail-of-tail action [High precision black hole scattering: Tutti Frutti vs worldline effective field theory, arXiv:2504.20204.] we compute several dynamical observables of binary systems (Delaunay Hamiltonian, scattering angle), at the 6.5 post-Newtonian accuracy and up to the eighth post-Minkowskian order. We find perfect agreement with previous self-force results, and (when inserting a recent high-post-Newtonian order derivation of radiated angular momentum [Scattering of a point mass by a Schwarzschild black hole: Radiated energy and angular momentum, arXiv:2507.03442.]) with state-of-the-art post-Minkowskian scattering results [Emergence of Calabi–Yau manifolds in high-precision black-hole scattering, Nature (London) 641, 603 (2025).].